By F. Ebrahimi
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Extra resources for Advances in Piezoelectric Transducers
Symbols D3, S1, T1 and E3 denote electric displacement, strain, stress and the electric field in the directions of the axis described by the subscript. After transformation of equation (24), force generated by the transducer can be described as: FP t c 11E Ap S1 x , t 1 t , (25) where: 1 t d31 E3 d31 UC t hp . (26) Symbol c11E denotes Young’s modulus of the transducer at zero/constant electric field (inverse of elasticity constant). UC(t) is an electric voltage on the capacitance Cp.
Ma, J. C. (2007a). 334-335, (2007) pp. H. & Ma, J. (2007b). C. & Ma, J. (2007c). High Amplitude Vibration of Piezoelectric Bending Actuators, J. H. & Ma, J. (2008). H. & Ma, J. (2009). 3, (March 2009), pp. L. & Ma J. (2010). Y. (1995). Study on the Multifrequency Langevin Ultrasonic Transducer, Ultrasonics, Vol. Y. (2004a). Effect of Electric Load Impedances on the Performance of Sandwich Piezoelectric Transducers, IEEE Trans. , Freq. Y. (2004b). M. (1987). D. T. (2010). A. F. P. (1964). P. & Wehr J.
Young’s modulus of the beam is denoted Eb. A piezoelectric transducer of length lp is bonded to the beam’s surface within the distance of x1 from a clamped end of the beam. The transducer is bonded by a glue layer of thickness hk and Kirchhoff’s modulus G. The glue layer has homogeneous properties in overall length. The system under consideration in both cases (with piezoelectric actuator or vibration damper) is presented in Fig. 1. In order to analyze vibration of the systems following assumptions were made: material of which the system is made is subjected to Hooke’s law, the system has a continuous, linear mass distribution, the system’s vibration is harmonic, planes of cross-sections that are perpendicular to the axis of the beam remain flat during deformation of the beam – an analysis is based on the Bernoulli’s hypothesis of flat cross-sections, displacements are small compared with the dimensions of the system.
Advances in Piezoelectric Transducers by F. Ebrahimi